Note the two clues:
8. Of the Art class and the second period class, one is in room 201 and the other is taught by Mr. Zamora.
9. The Art class is either the class in room 129 or Mr. Zamora's class.

Clue 8 can be broken down into two statements:
8A. The Art class is either the class in room 201 or taught by Mr. Zamora's class.
8B. The second period class is either the class in room 201 or taught by Mr. Zamora's class.

Combinding the two similar "Either" statements
8A. The Art class is either the class in room 201 or by Mr. Zamora's class.
9. The Art class is either the class in room 129 or Mr. Zamora's class.

Since both statements are true, the only answer for the Art class is that it is being taught by Mr. Zamora.